If statements prefixed with a modal operator were all treated as false, on the other hand, then if the standard interdefinitions applied, violations of the law of non-contradiction could be generated.
One would maintain that modal operators (and associated pieces of language like essential predication, counterfactual conditionals, and perhaps other things like assignments of probabilities) lacked literal application: that all statements prefixed with a modal operator were either uniformly literally truthvalueless or uniformly literally false.
If the modal operator is an epistemic 'must', as she suggests, bare conditionals are a species of strict conditional — something like 'all live A-possibilities are C-possibilities'.
It is hard to know how the issue of whether or not "according to PW…" should count as a modal operator is to be decided: in any case, it will not be further pursued here.
This means that, at non-normal worlds, formulas of the form £A, with £ a modal operator, are not evaluated recursively depending on the truth value of A at other (accessible) worlds, but get assigned their truth value directly.
Further, modal operators were typically construed as operating on the intensions of the sentences they embed, and so those intensions could plausibly be thought of as possessing modal properties.
In fact, Field has argued that if modal operators were invoked in the formulation of scientific theories, not only their mathematical content, but also their physical content would be nominalized (Field 1989).
In Lewis's theory of modality, then, modal operators are understood semantically to be quantifiers over concrete worlds, predicates denote intensions understood as sets of (n-tuples of) parts of those worlds, and sentences involving de re modalities are understood in terms of counterparts.
The properties of the InfoNeed operator and its relationships to other mental modal operators are examined, four types of information needs are formally identified, and axioms for anticipating the information needs of other agents are proposed and justified.
The two modal operators are connected by the usual equivalence $ENLpMNp$.
One recent worked-out modal fictionalist approach which explicitly analyses the relevant "according to the modal fiction" operator in terms of modal operators is Divers 1999b.
